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Delayed fluorescence and delayed excimer fluorescence from fluid solutions of poly(2-vinylnaphthalene) in the nanosecond time regime
Volume 157, number 3
CHEMICAL PHYSICS LETTERS
5 May 1989
DELAYED FLUORESCENCE AND DELAYED EXCIMER FLUORESCENCE FROM FLUID SOLUTIONS OF POLY(2-VINYLNAPHTHALENE) IN THE NANOSECOND TIME REGIME Dilip K. CHAKRABORTY
and Richard D. BURKHART
Department of Chemistry, University o_fNevada-Rena, Reno, NV 69557, USA
Received 24 January 1989; in final form 4 February 1989
The time dependence of delayed fluorescence (DF) and delayed excimer fluorescence (DEF) of poly( 2-vinylnaphthalene) (P2VN) has been measured m fluid solution at ambient temperature. Within the time resolution of the apparatus, the DF decreases monotonically with time but DEF exhibits a maximum intensity near 300 ns. The time dependence of the DEF signal suggests that one of the triplet partners must be trapped prior to the annihilative event. Model calculations have been carried out yielding a trapping rate constant of (2.0k0.5) x 109M-’ s-r. The rate-controlling step for triplet trapping may involve internal rotation of the chain backbone,
1. Introduction General descriptions of photoluminescence processes in polymers have been thoroughly described in the literature [ 1,2] but in the present case attention will be focused upon delayed fluorescence (DF) which arises by triplet-triplet annihilation. Triplet photophysical properties of polymers have been the subject of numerous experimental investigations usually in the millisecond time scale. It is only in recent years that more attention has been paid to these properties using time resolutions in the sub-millisecond range [ 3 1. Since the lifetimes of triplet state species have the reputation of being quite long, it is reasonable to ask why one needs to explore their behavior at times significantly shorter than the millisecond range. The answer to this question lies in the nature of the polymer itself. Because of the random coiling associated with polymer molecules, there is always a high local density of chromophore units even if the gross concentration of chromophores is quite small. For this reason triplet energy transfer between chromophore units occurs with high efficiency in polymeric systems and so do second-order processes involving exciton-exciton interactions. In addition to DF, fluid solutions of P2VN also emit delayed excimer fluorescence (DEF) the de0 009-2614/89/$ (North-Holland
03.50 0 Elsevier Science Publishers Physics Publishing Division )
tailed origin of which is uncertain. Two possible pathways for DEF production are: (I) Homo-annihilation between two mobile triplet excitons followed by trapping of the excited singlet exciton at an excimer-forming site. (II) Trapping of a mobile triplet exciton at an extimer-forming site followed by hetero-annihilation between a mobile triplet exciton and a trapped triplet exciton. It is reasonable to expect that the rates of the annihilative processes will be the same for either mechanism since both will depend upon rates of triplet exciton migration. A difference in time characteristics might be encountered, however, due to expected different rates of exciton trapping of a singlet exciton versus a triplet exciton. Singlet energy migration occurs primarily by the longer-range dipolar mechanism known as the Fdrster mechanism [ 41 as opposed to the relatively shorter-range process of electron exchange usually found for triplets [ 51. A primary purpose of this project, therefore, was to examine these time dependences in an attempt to determine which mechanism is dominant in fluid solutions at ambient temperature. In addition, it was planned to evaluate as many of the relevant specific rate constants as possible.
B.V.
189
Volume 157, number 3
5 May 1989
CHEMICAL PHYSICS LETTERS
2. Experimental In connection with an earlier project [6] P2VN was prepared in this laboratory using standard techwith n-butyllithniques of anionic polymerization ium as initiator. The purification of the solvents used benzene and 2-methyltetrahydrofuran here, (MTHF), has been previously described [ 71. Solutions of the polymer in MTHF were degassed using several freeze-pump-thaw cycles, after which the sample was sealed off under vacuum. The solution was then tipped into a 10 mm pathlength rectangular quartz cell which had previously been joined by a T connection to the freeze-down bulb. The source of excitation was a Tachisto model 401 XR XeCl excimer laser. The emission signal from the sample was passed through a Spex model 168OB monochromator using a 0.18 nm bandpass. It was then detected by a 4 ns rise-time photomultiplier. The output of the photomultiplier was directly fed into a Nicolet model 12/70 signal avcrager using a 50 Q terminating resistor to eliminate artificial delays in signal arrival time. The fastest filtration setting of 10 MHz was also used. The data were always corrected
for background contributions obtained from experiments using solvent only in the sample cell. Data from the Nicolet system were transferred to a microcomputer for further processing.
3. Experimental
monotonically
WAVELENGTH
520.0
570.0
(NM)
Fig. 1.Delayed luminescence spectra of PZVN 2.92 x lo-’ M m monomer units in MTHF at ambient temperature. Delay times after excitation are (a) 175, (b) 300 and (c) 600 ns.
DEF signals with time were examined at wavelengths where each component is relatively uncontaminated by overlap from the other (340 nm for DF and 425 nm for DEF). The results are demonstrated in figs. 2 and 3. In these figures the solid lines
x ul
c Q,
c
with time. On the other hand,
the DEF signal goes through a build-up period before reaching the maximum intensity near 300 ns, after which it decays monotonically with time. It should be mentioned here that all of these spectra are in the same intensity scale. The behavior of the DF and 190
,,-“T’r, W,,,‘“~~“~rn’,’ 370.0 420 0 4/u Cj
results
Fig. 1 shows the DF and DEF spectra from P2VN solutions at various delay times. The spectra can be divided into two distinctive regions. One is a structured part due to DF at lower wavelengths and the other a broad structureless region due to DEF at longer wavelengths. The primary observation upon which all of the subsequent discussion is based is that DF and DEF components display different characteristics with respect to time. It was found that, even at the shortest delay times of 100 ns, the DF signal decays
0 0 320 0
Fig. 2. Decay of delayed fluorescence intensity at 340 nm. The curve with open circles is the experimental result. The solid curves are calculated curves wdh k,,['F&lequal to 2.5 x lo6 SC' (above thedashed curve) and 3.5~ IO6 SC’ (below thedashed curve). dashed
Volume 157, number 3
CHEMICAL PHYSICS LETTERS
5 May 1989
of the photophysics of these systems leaves no doubt that the species in question are chromophores in the lowest triplet state. In the case of the DF emission at 340 nm there must also be a build-up period as triplet states are produced by intersystem crossing from the excited singlet state. Evidently this build-up occurs on a time period too short to be measured by our apparatus. It is proposed that the build-up period associated with the production of DEF is a direct result of a corresponding build-up in the population of trapped triplets. That is, the second mechanism described above is the primary one at work here and may be summarized as follows: kl IS*--
‘S,+hy
(orheat),
(1)
hwz IS* Fig. 3. Decay of delayed fluorescence intensity at 425 nm. The dashed curve with open circles is the experimental curve. The solid curves are for k,,[‘E,] equal to (a) 2.5~ LO6s-’ and (b) 3.5x 106s-‘.
*s* + ‘So )
T, +T, k,r T, +‘Eo -T,,>
Since our goal is to understand the unique aspects of the DF and DEF emissions at short delay times, it is necessary to be concerned about overlapping between prompt fluorescence and delayed fluorescence in the spectra which have been recorded. Although the fluorescence lifetime of single naphthalene molecules is on the order of 100 ns, the lifetime of the first excited singlet state of vinylnaphthalene homopolymers is much shorter. Poly ( 1-vinylnaphthalene), for example, has a fluorescence lifetime of 7.4 ns and the lifetime of the excimer fluorescence is 43 ns [ 81. Using the reasonable assumption that the excited singlet state lifetime for P2VN is similar to P 1VN, delay times used in this work are sufficiently large to insure that no contamination of DF or DEF from prompt fluorescence is occurring. The fact that the DEF intensity exhibits an early build-up period (up to about 300 ns) can only be explained if the luminescence signal is due to species which are increasing with time. Our understanding
(3) (4)
k2 T, +T,,+ ‘E*+‘E,+hv
4. Discussion
(2)
k2
are curves calculated using methods to be described below.
T, ,
‘E*+‘S,, , (or heat) .
(5) (6)
In these equations ‘S* is the excited singlet, ‘E* is the singlet excimer, T, is the mobile triplet, T,, is the trapped triplet, ‘E, is the trapping site in the ground state, and ‘So is the ground state of an independent chromophore. Eqs. ( 1) and (2) describe all first-order processes taking place from the excited singlet state. Eq. (4) describes the trapping of mobile triplets to form the trapped triplet. Eqs. (3) and (5) describe the annihilation processes responsible for DF and DEF respectively. It is permissable to use the same rate constant for both steps since the rate in each case depends upon the diffusion rate of the mobile exciton. The fact that both reactants in step (3 ) are diffusing is offset by the fact that the a priori probability of like-like encounters is one-half that of encounters between distinct species. Eq. (6 ) represents decay of the singlet excimer. In order to see that our model is consistent with the experimental results it is necessary to calculate the concentration of triplets as a function of time. The DF intensity at 340 nm is proportional to the square of the T, concentration, whereas the DEF in191
Volume 157,number 3
tensity at 425 m-n is proportional to the product of the concentrations of T, and T,,. The necessary differential equation for the formation and decay of T, is
-kr[‘Eol ITI 1 >
(7)
where [IS*] = [‘S(O)] exp( -k&) and kprl= k, + k,,,. Here [ ‘S (0) ] is the concentration of excited singlet states at t = 0. The differential equation describing the time dependence of T,, is
d[T,rlld~=kr[‘Eol [TI 1--kz [Ttrl [T, 1 -
(8)
This set of coupled first-order differential equations was solved numerically by using the fourth-order Runge-Kutta method [ 91 #’ with the initial conditionthat [T,(O)]=[T,,(O)]=O.ThevaIueofk,has been determined from independent experiments using time-dependent triplet-triplet absorption. It may be mentioned here that in order to determine kZ a reevaluation was made of the molar extinction coefficient of naphthalene triplets for P2VN in fluid solution at ambient temperature. The value obtained at 425 nm ( 12500 M-’ cm-‘) using a ground state depletion method is in excellent agreement with an earlier determination using triplet sensitization [ lo]. The value of k, used was the same as for PlVN [ 8 ] and the value of k,,, was estimated from the triplet quantum yield value given by Bensasson and coworkers [IO]. In the calculations, k,[ ‘E,,] and kIsc [ ‘S(O) ] are taken as variable parameters. Solutions of eqs. (7) and (8) give the concentrations of T, and T,, as a function of time. These are then used to calculate the DF intensities as a function of time. The calculated DF intensity is multiplied by a constant chosen in order to match the experimental intensity at some given time. This constant incorporates the yield of excited singlets formed upon each annihilative event, the radiative yield from these singlets and geometrical variables associated with light collection optics. Typical results are shown in figs. 2 and 3 by solid curves. Numerical analysis shows that for k,[ ‘E,] = 2.5 X 1O6 s-’ the rising part of fig. 3 is reproduced ” The extension to coupled equations was provided by Professor H.K. Shin.
192
5 May 1989
CHEMICALPHYSICSLETTEKS
well whereas a value of 3.5 x 1O6 reproduces the decay portion. It was interesting to learn that the curve shape is not very sensitive to k,,,[‘S(O)]. A fixed value I .0x lo3 M s- ’ was used throughout the calculations. For fig. 2 it can be seen that either value of k,, [ ‘Eo] gives satisfactory results. Since the maximum number of dimeric trap sites is equal to onehalf of the molar concentration of chromophore units, this estimate for [ ‘E,] yields a lower limit for k,, of 1.7x109t02.4x109M-1s-‘.Thevaluesofthedifferent parameters used or derived from the best fit to these experimental data are presented in table I. We are aware of no previous dctcrminations of a rate constant for trapping of triplet excitons at an extimer-forming site in a polymer chain. It may be noted, however, that a rate constant for trapping of singlet excitons in poly (N-vinylcarbazole) was found [ 111 to be an order of magnitude larger than the k,, found here. It is of some interest to note that the calculations predict that a maximum should occur in the DF time profile near 30 ns. It is especially noteworthy that the rate constant for triplet trapping obtained in this study is at least a factor of ten larger than the rate constant for triplet-triplet annihilation. It had been assumed that the rate of exciton migration would be rate controlling for both processes but apparently this is not the case. Evidently a more rapid channel is available for the trapping process and, in reviewing the possibilities, it seems likely that internal rotations around backbone carbon atoms may provide a viable mechanism for the trapping process. Thus, during the time that a triplet exciton resides at a given chromophore, a Table 1 Specific rate constants used or derived by fittmg experimental data Constant
Value
k, a1(SC’) kz (Mm’s_‘)
8.6x 103 3.3x 10s 1.4x 108b, (2.5-3.5)x 106”’ (1.7-2.4)x 109d’
k, (s-l) kJ’E,l (s-’ )
k,, (M-‘sv’)
a1Specific rate constant for first-order triplet decay. ‘) Ref. [ 81. ‘) Obtained by fitting of experimental curve, d1By assuming the concentration of trap sites equals one-halfthe molar concentration of chromophores.
Volume 157.number 3
CHEMICALPHYSICSLETTERS
neighbor or near neighbor may rotate into a conformation suitable for trap formation. If this is the case, rate constants for trap formation may provide useful information with regard to rates of internal rotation for given polymer-solvent systems but more experimental work will be required to confirm this as a reliable mechanistic interpretation.
5. Conclusion
5 May 1989
nation of a trapping rate constant for triplet excitons in a polymer molecule.
Acknowledgement This work was supported by the US Department of Energy under grant No. DE-FG08-84ER45 107.
References [I ] J.W. Guillet, Polymer photophysics and photochemistry
An analysis of delayed fluorescence signals in the submicrosecond range shows that the DEF signal rises with time up to 300 ns and then decreases monotonically. This behavior indicates that the mechanism of DEF production involves trapping of mobile triplet excitons followed by hetero-annihilation between a trapped triplet exciton and a mobile one. By numerical integration of the relevant rate equations and the subsequent manipulation of adjustable parameters, a good fit between calculated and experimental DF and DEF intensities is obtained. The ratecontrolling process for the trapping of triplets may involve backbone rotations of the polymer chain. To the best of our knowledge this is the first determi-
(Cambridge Univ. Press, Cambridge, 1985). [2] W. Klopffer, Introduction to polymer spectroscopy (Springer, Berlin, 1984). [3 JR.D. Burkhart, Macromolecules 16 (1983) 820. [4] Th. Fijrster, Ann. Physik 2 (1948) 55. [5] D.L. Dexter,J. Chem. Phys. 21 (1953) 836. [ 6 ] T.J.K.S. Siu and R.D. Burkhart, Macromolecules, in press. [7]R.D. Burkhart, G.W. Haggquist and S.E. Webber, Macromolecules 20 (1987) 3012. [S] K.P. Ghiggino, R.D. Wright and D. Phillips, Chem. Phys. Letters 53 (1978) 552. [9] R.L. Burden, J.D. Faires and A.C. Reynolds, Numerical analysis, 2nd Ed. (PWS Publishers. 1981) p. 200. [ IO] R.V. Bensasson, J.C. Ronfard-Haret, E.J. Land and S.E. Webber, Chem. Phys. Letters 68 ( 1979) 438. [ 11 ] A. Itaya, H. Sakai and H. Masuhara, Chem. Phys. Letters 146 (1988) 570.
193
CHEMICAL PHYSICS LETTERS
5 May 1989
DELAYED FLUORESCENCE AND DELAYED EXCIMER FLUORESCENCE FROM FLUID SOLUTIONS OF POLY(2-VINYLNAPHTHALENE) IN THE NANOSECOND TIME REGIME Dilip K. CHAKRABORTY
and Richard D. BURKHART
Department of Chemistry, University o_fNevada-Rena, Reno, NV 69557, USA
Received 24 January 1989; in final form 4 February 1989
The time dependence of delayed fluorescence (DF) and delayed excimer fluorescence (DEF) of poly( 2-vinylnaphthalene) (P2VN) has been measured m fluid solution at ambient temperature. Within the time resolution of the apparatus, the DF decreases monotonically with time but DEF exhibits a maximum intensity near 300 ns. The time dependence of the DEF signal suggests that one of the triplet partners must be trapped prior to the annihilative event. Model calculations have been carried out yielding a trapping rate constant of (2.0k0.5) x 109M-’ s-r. The rate-controlling step for triplet trapping may involve internal rotation of the chain backbone,
1. Introduction General descriptions of photoluminescence processes in polymers have been thoroughly described in the literature [ 1,2] but in the present case attention will be focused upon delayed fluorescence (DF) which arises by triplet-triplet annihilation. Triplet photophysical properties of polymers have been the subject of numerous experimental investigations usually in the millisecond time scale. It is only in recent years that more attention has been paid to these properties using time resolutions in the sub-millisecond range [ 3 1. Since the lifetimes of triplet state species have the reputation of being quite long, it is reasonable to ask why one needs to explore their behavior at times significantly shorter than the millisecond range. The answer to this question lies in the nature of the polymer itself. Because of the random coiling associated with polymer molecules, there is always a high local density of chromophore units even if the gross concentration of chromophores is quite small. For this reason triplet energy transfer between chromophore units occurs with high efficiency in polymeric systems and so do second-order processes involving exciton-exciton interactions. In addition to DF, fluid solutions of P2VN also emit delayed excimer fluorescence (DEF) the de0 009-2614/89/$ (North-Holland
03.50 0 Elsevier Science Publishers Physics Publishing Division )
tailed origin of which is uncertain. Two possible pathways for DEF production are: (I) Homo-annihilation between two mobile triplet excitons followed by trapping of the excited singlet exciton at an excimer-forming site. (II) Trapping of a mobile triplet exciton at an extimer-forming site followed by hetero-annihilation between a mobile triplet exciton and a trapped triplet exciton. It is reasonable to expect that the rates of the annihilative processes will be the same for either mechanism since both will depend upon rates of triplet exciton migration. A difference in time characteristics might be encountered, however, due to expected different rates of exciton trapping of a singlet exciton versus a triplet exciton. Singlet energy migration occurs primarily by the longer-range dipolar mechanism known as the Fdrster mechanism [ 41 as opposed to the relatively shorter-range process of electron exchange usually found for triplets [ 51. A primary purpose of this project, therefore, was to examine these time dependences in an attempt to determine which mechanism is dominant in fluid solutions at ambient temperature. In addition, it was planned to evaluate as many of the relevant specific rate constants as possible.
B.V.
189
Volume 157, number 3
5 May 1989
CHEMICAL PHYSICS LETTERS
2. Experimental In connection with an earlier project [6] P2VN was prepared in this laboratory using standard techwith n-butyllithniques of anionic polymerization ium as initiator. The purification of the solvents used benzene and 2-methyltetrahydrofuran here, (MTHF), has been previously described [ 71. Solutions of the polymer in MTHF were degassed using several freeze-pump-thaw cycles, after which the sample was sealed off under vacuum. The solution was then tipped into a 10 mm pathlength rectangular quartz cell which had previously been joined by a T connection to the freeze-down bulb. The source of excitation was a Tachisto model 401 XR XeCl excimer laser. The emission signal from the sample was passed through a Spex model 168OB monochromator using a 0.18 nm bandpass. It was then detected by a 4 ns rise-time photomultiplier. The output of the photomultiplier was directly fed into a Nicolet model 12/70 signal avcrager using a 50 Q terminating resistor to eliminate artificial delays in signal arrival time. The fastest filtration setting of 10 MHz was also used. The data were always corrected
for background contributions obtained from experiments using solvent only in the sample cell. Data from the Nicolet system were transferred to a microcomputer for further processing.
3. Experimental
monotonically
WAVELENGTH
520.0
570.0
(NM)
Fig. 1.Delayed luminescence spectra of PZVN 2.92 x lo-’ M m monomer units in MTHF at ambient temperature. Delay times after excitation are (a) 175, (b) 300 and (c) 600 ns.
DEF signals with time were examined at wavelengths where each component is relatively uncontaminated by overlap from the other (340 nm for DF and 425 nm for DEF). The results are demonstrated in figs. 2 and 3. In these figures the solid lines
x ul
c Q,
c
with time. On the other hand,
the DEF signal goes through a build-up period before reaching the maximum intensity near 300 ns, after which it decays monotonically with time. It should be mentioned here that all of these spectra are in the same intensity scale. The behavior of the DF and 190
,,-“T’r, W,,,‘“~~“~rn’,’ 370.0 420 0 4/u Cj
results
Fig. 1 shows the DF and DEF spectra from P2VN solutions at various delay times. The spectra can be divided into two distinctive regions. One is a structured part due to DF at lower wavelengths and the other a broad structureless region due to DEF at longer wavelengths. The primary observation upon which all of the subsequent discussion is based is that DF and DEF components display different characteristics with respect to time. It was found that, even at the shortest delay times of 100 ns, the DF signal decays
0 0 320 0
Fig. 2. Decay of delayed fluorescence intensity at 340 nm. The curve with open circles is the experimental result. The solid curves are calculated curves wdh k,,['F&lequal to 2.5 x lo6 SC' (above thedashed curve) and 3.5~ IO6 SC’ (below thedashed curve). dashed
Volume 157, number 3
CHEMICAL PHYSICS LETTERS
5 May 1989
of the photophysics of these systems leaves no doubt that the species in question are chromophores in the lowest triplet state. In the case of the DF emission at 340 nm there must also be a build-up period as triplet states are produced by intersystem crossing from the excited singlet state. Evidently this build-up occurs on a time period too short to be measured by our apparatus. It is proposed that the build-up period associated with the production of DEF is a direct result of a corresponding build-up in the population of trapped triplets. That is, the second mechanism described above is the primary one at work here and may be summarized as follows: kl IS*--
‘S,+hy
(orheat),
(1)
hwz IS* Fig. 3. Decay of delayed fluorescence intensity at 425 nm. The dashed curve with open circles is the experimental curve. The solid curves are for k,,[‘E,] equal to (a) 2.5~ LO6s-’ and (b) 3.5x 106s-‘.
*s* + ‘So )
T, +T, k,r T, +‘Eo -T,,>
Since our goal is to understand the unique aspects of the DF and DEF emissions at short delay times, it is necessary to be concerned about overlapping between prompt fluorescence and delayed fluorescence in the spectra which have been recorded. Although the fluorescence lifetime of single naphthalene molecules is on the order of 100 ns, the lifetime of the first excited singlet state of vinylnaphthalene homopolymers is much shorter. Poly ( 1-vinylnaphthalene), for example, has a fluorescence lifetime of 7.4 ns and the lifetime of the excimer fluorescence is 43 ns [ 81. Using the reasonable assumption that the excited singlet state lifetime for P2VN is similar to P 1VN, delay times used in this work are sufficiently large to insure that no contamination of DF or DEF from prompt fluorescence is occurring. The fact that the DEF intensity exhibits an early build-up period (up to about 300 ns) can only be explained if the luminescence signal is due to species which are increasing with time. Our understanding
(3) (4)
k2 T, +T,,+ ‘E*+‘E,+hv
4. Discussion
(2)
k2
are curves calculated using methods to be described below.
T, ,
‘E*+‘S,, , (or heat) .
(5) (6)
In these equations ‘S* is the excited singlet, ‘E* is the singlet excimer, T, is the mobile triplet, T,, is the trapped triplet, ‘E, is the trapping site in the ground state, and ‘So is the ground state of an independent chromophore. Eqs. ( 1) and (2) describe all first-order processes taking place from the excited singlet state. Eq. (4) describes the trapping of mobile triplets to form the trapped triplet. Eqs. (3) and (5) describe the annihilation processes responsible for DF and DEF respectively. It is permissable to use the same rate constant for both steps since the rate in each case depends upon the diffusion rate of the mobile exciton. The fact that both reactants in step (3 ) are diffusing is offset by the fact that the a priori probability of like-like encounters is one-half that of encounters between distinct species. Eq. (6 ) represents decay of the singlet excimer. In order to see that our model is consistent with the experimental results it is necessary to calculate the concentration of triplets as a function of time. The DF intensity at 340 nm is proportional to the square of the T, concentration, whereas the DEF in191
Volume 157,number 3
tensity at 425 m-n is proportional to the product of the concentrations of T, and T,,. The necessary differential equation for the formation and decay of T, is
-kr[‘Eol ITI 1 >
(7)
where [IS*] = [‘S(O)] exp( -k&) and kprl= k, + k,,,. Here [ ‘S (0) ] is the concentration of excited singlet states at t = 0. The differential equation describing the time dependence of T,, is
d[T,rlld~=kr[‘Eol [TI 1--kz [Ttrl [T, 1 -
(8)
This set of coupled first-order differential equations was solved numerically by using the fourth-order Runge-Kutta method [ 91 #’ with the initial conditionthat [T,(O)]=[T,,(O)]=O.ThevaIueofk,has been determined from independent experiments using time-dependent triplet-triplet absorption. It may be mentioned here that in order to determine kZ a reevaluation was made of the molar extinction coefficient of naphthalene triplets for P2VN in fluid solution at ambient temperature. The value obtained at 425 nm ( 12500 M-’ cm-‘) using a ground state depletion method is in excellent agreement with an earlier determination using triplet sensitization [ lo]. The value of k, used was the same as for PlVN [ 8 ] and the value of k,,, was estimated from the triplet quantum yield value given by Bensasson and coworkers [IO]. In the calculations, k,[ ‘E,,] and kIsc [ ‘S(O) ] are taken as variable parameters. Solutions of eqs. (7) and (8) give the concentrations of T, and T,, as a function of time. These are then used to calculate the DF intensities as a function of time. The calculated DF intensity is multiplied by a constant chosen in order to match the experimental intensity at some given time. This constant incorporates the yield of excited singlets formed upon each annihilative event, the radiative yield from these singlets and geometrical variables associated with light collection optics. Typical results are shown in figs. 2 and 3 by solid curves. Numerical analysis shows that for k,[ ‘E,] = 2.5 X 1O6 s-’ the rising part of fig. 3 is reproduced ” The extension to coupled equations was provided by Professor H.K. Shin.
192
5 May 1989
CHEMICALPHYSICSLETTEKS
well whereas a value of 3.5 x 1O6 reproduces the decay portion. It was interesting to learn that the curve shape is not very sensitive to k,,,[‘S(O)]. A fixed value I .0x lo3 M s- ’ was used throughout the calculations. For fig. 2 it can be seen that either value of k,, [ ‘Eo] gives satisfactory results. Since the maximum number of dimeric trap sites is equal to onehalf of the molar concentration of chromophore units, this estimate for [ ‘E,] yields a lower limit for k,, of 1.7x109t02.4x109M-1s-‘.Thevaluesofthedifferent parameters used or derived from the best fit to these experimental data are presented in table I. We are aware of no previous dctcrminations of a rate constant for trapping of triplet excitons at an extimer-forming site in a polymer chain. It may be noted, however, that a rate constant for trapping of singlet excitons in poly (N-vinylcarbazole) was found [ 111 to be an order of magnitude larger than the k,, found here. It is of some interest to note that the calculations predict that a maximum should occur in the DF time profile near 30 ns. It is especially noteworthy that the rate constant for triplet trapping obtained in this study is at least a factor of ten larger than the rate constant for triplet-triplet annihilation. It had been assumed that the rate of exciton migration would be rate controlling for both processes but apparently this is not the case. Evidently a more rapid channel is available for the trapping process and, in reviewing the possibilities, it seems likely that internal rotations around backbone carbon atoms may provide a viable mechanism for the trapping process. Thus, during the time that a triplet exciton resides at a given chromophore, a Table 1 Specific rate constants used or derived by fittmg experimental data Constant
Value
k, a1(SC’) kz (Mm’s_‘)
8.6x 103 3.3x 10s 1.4x 108b, (2.5-3.5)x 106”’ (1.7-2.4)x 109d’
k, (s-l) kJ’E,l (s-’ )
k,, (M-‘sv’)
a1Specific rate constant for first-order triplet decay. ‘) Ref. [ 81. ‘) Obtained by fitting of experimental curve, d1By assuming the concentration of trap sites equals one-halfthe molar concentration of chromophores.
Volume 157.number 3
CHEMICALPHYSICSLETTERS
neighbor or near neighbor may rotate into a conformation suitable for trap formation. If this is the case, rate constants for trap formation may provide useful information with regard to rates of internal rotation for given polymer-solvent systems but more experimental work will be required to confirm this as a reliable mechanistic interpretation.
5. Conclusion
5 May 1989
nation of a trapping rate constant for triplet excitons in a polymer molecule.
Acknowledgement This work was supported by the US Department of Energy under grant No. DE-FG08-84ER45 107.
References [I ] J.W. Guillet, Polymer photophysics and photochemistry
An analysis of delayed fluorescence signals in the submicrosecond range shows that the DEF signal rises with time up to 300 ns and then decreases monotonically. This behavior indicates that the mechanism of DEF production involves trapping of mobile triplet excitons followed by hetero-annihilation between a trapped triplet exciton and a mobile one. By numerical integration of the relevant rate equations and the subsequent manipulation of adjustable parameters, a good fit between calculated and experimental DF and DEF intensities is obtained. The ratecontrolling process for the trapping of triplets may involve backbone rotations of the polymer chain. To the best of our knowledge this is the first determi-
(Cambridge Univ. Press, Cambridge, 1985). [2] W. Klopffer, Introduction to polymer spectroscopy (Springer, Berlin, 1984). [3 JR.D. Burkhart, Macromolecules 16 (1983) 820. [4] Th. Fijrster, Ann. Physik 2 (1948) 55. [5] D.L. Dexter,J. Chem. Phys. 21 (1953) 836. [ 6 ] T.J.K.S. Siu and R.D. Burkhart, Macromolecules, in press. [7]R.D. Burkhart, G.W. Haggquist and S.E. Webber, Macromolecules 20 (1987) 3012. [S] K.P. Ghiggino, R.D. Wright and D. Phillips, Chem. Phys. Letters 53 (1978) 552. [9] R.L. Burden, J.D. Faires and A.C. Reynolds, Numerical analysis, 2nd Ed. (PWS Publishers. 1981) p. 200. [ IO] R.V. Bensasson, J.C. Ronfard-Haret, E.J. Land and S.E. Webber, Chem. Phys. Letters 68 ( 1979) 438. [ 11 ] A. Itaya, H. Sakai and H. Masuhara, Chem. Phys. Letters 146 (1988) 570.
193